Self-testing is a device-independent technique that allows for verification of unknown quantum systems only when observed correlations achieve some quantum supremum. In this paper, we present self-testing schemes for a class of multipartite Bell inequalities with a specific structure, which we refer to as the unit. Our research is based on the graph-theoretic approach, where correlations are characterized via Lovász theta body in the framework of exclusivity graphs. The derived statements are subsequently applied to prove the self-testability of $N$-partite Mermin-Ardehali-Belinskiǐ-Klyshko (MABK) family of Bell inequalities. In particular, we take special cases to demonstrate that the maximal violation of the multipartite MABK inequality is a self-test for the corresponding multipartite Greenberger-Horne-Zeilinger (GHZ) state. Moreover, we propose a device-independent verification algorithm for distributed blind quantum computation in the noisy intermediate-scale quantum era combined with multipartite GHZ state self-testing, where multiple quantum servers are involved and work in collaboration to reduce the burden on a single server.

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• Quantum algorithms
• Quantum correlations in quantum information
• Quantum verification
• Quantum many-body systems
• Graph theory